Description of fast matrix multiplication algorithm: ⟨10×21×21:2640⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 30 X^{4} Y^{6} Z^{4} + 3 X^{2} Y^{2} Z^{10} + 174 X^{4} Y^{4} Z^{4} + 9 X^{2} Y^{2} Z^{8} + 12 X^{6} Y^{2} Z^{2} + 3 X^{4} Y^{4} Z^{2} + 84 X^{2} Y^{6} Z^{2} + 21 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{4} Z^{2} + 57 X^{4} Y^{2} Z^{2} + 423 X^{2} Y^{4} Z^{2} + 45 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 6 X Y^{2} Z^{5} + 6 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{4} Z + 60 X^{2} Y^{3} Z^{2} + 42 X Y^{4} Z^{2} + 18 X Y^{2} Z^{4} + 6 X Y Z^{5} + 24 X^{3} Y^{2} Z + 417 X^{2} Y^{2} Z^{2} + 150 X Y^{4} Z + 6 X Y^{2} Z^{3} + 18 X Y Z^{4} + 24 X^{3} Y Z + 120 X^{2} Y^{2} Z + 48 X Y^{3} Z + 132 X Y^{2} Z^{2} + 6 X Y Z^{3} + 114 X^{2} Y Z + 288 X Y^{2} Z + 90 X Y Z^{2} + 138 X Y Z

Algorithm definition

The algorithm ⟨10×21×21:2640⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨5×7×7:176⟩.

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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